Dragon scale has to do with the scaling, nothing with the fins; they can be on long finned fish or short finned fish.
Here is a Dragon scale Plakat (plakat just meaning short fins)
He also happens to be a HMPK as well (halfmoon plakat) Halfmoon just has to do with the finnage that makes the D shape like the boy in my avatar.
This boy: http://www.bettas-jimsonnier.com/images/BlackHM+.jpg
is a regular scaled Betta but has a HM shape.
Now here's HM plakat:
So this boy above just has the D shape to his tail fin making him a Halfmoon betta and because he's got short fins that means he's a Plakat or PK.
Here's a longer finned Dragon Scale boy: http://imageshack.us/a/img211/7475/f...1369408679.jpg
notice the white scales, see how thick they are? That denotes a Dragon scale. He's also noted as a Full Masked Dragon Scale or DS. See how his scales go all on his head? And then look back to the first picture, notice the stripe where there are no white scales? That's refered to as a "skunk" stripe and is very common on DS Betta's if their scales don't cover all on their head.
And here is my boy Aero:
Notice he's got spots of black on his head? He used to have a skunk stripe but now his scales are filling in, soon he'll also have a Full Mask.